%0 Journal Article
%T The solution of the Kato problem for degenerate elliptic operators with Gaussian bounds
%A D. Cruz-Uribe
%A C. Rios
%J Mathematics
%D 2009
%I arXiv
%X We prove the Kato conjecture for degenerate elliptic operators in R^n. More precisely, we consider the divergence form operator L_w = -1/w div (wA) grad, where w is a Muckenhoupt A_2 weight and A is a complex valued n x n matrix which is bounded and uniformly elliptic. We show that if the associated semigroup satisfies Gaussian upper bounds, then the Kato square root estimate holds.
%U http://arxiv.org/abs/0907.2947v1